This invention relates to optical devices such as reflecting mirror telescopes that employ a single multifaceted objective surface on which are located multiple mirrors, each mirror being oriented nearly orthogonal to the optical axis and whose location along the optical axis can be moved, independent of and unconstrained by the physical locations of the remaining mirrors. In the case of multiple mirror telescopes, moving the mirrors permits compensation for aberrations, induced by the propagation of light from a stellar object through a turbulent atmosphere, to a degree sufficient to establish a continually focused image of the stellar object. Such a telescope is disclosed in an article entitled Proceedings of SPIE, The International Society for Optical Engineers, pg. 109-0116 (1982) Vol. 332, pg. 109-116, University of California Ten Meter Telescope Project, by Jerry E. Nelson.
FIG. 1 illustrates a standard single mirror parabolic reflector 1 for a telescope. The objective surface 2 is described by the equation EQU Z=(X.sup.2 +Y.sup.2)/(2r) for X.sup.2 +Y.sup.2 .ltoreq.D.sup.2 (1)
where r is the radius of curvature of the parabolic surface and D is the diameter of the parabolic surface. In conventional telescopes, D&lt;&lt;r (i.e. D is small compared with r) and all observed stellar point objects lie in a direction almost parallel to the optical axis, which coincides with the Z axis. It is well known to those skilled in the art that an observed stellar point object p located in a direction specified by the unit vector EQU V=(cos(.theta.)sin(.phi.),sin(.theta.)sin(.phi.),cos(.phi.)) (2)
will form an image I(p) centered about the point EQU Q=(Fcos(.theta.)sin(.phi.),Fsin(.theta.)sin(.phi.),F) (3)
and lying within the focal plane defined by the equation Z=F where F=r/2 is the focal length of the telescope, .phi. is the angle between the Z axis and the vector V and .theta. is the angle between the X axis and the projection of vector V onto the X, Y plane. See, for example, the text, "Introduction to Fourier Optics", Joseph Goodman, McGraw Hill, NY, 1968.
In the absence of aberrations induced by either the propagation of light through a turbulent atmosphere or by irregularities in the shape of the telescope objective, the distribution of light intensity in the focal plane of the telescope is described by an Airy pattern. See, the above cited Goodman text at pages 64, 65. Light intensity falls off from a maximum value at the center Q of the image I(p) to a value of zero in a circle centered at Q and having radius (j.sub.1 /.pi.)FL/D where L=wavelength of light emanating from p and j.sub.1 .apprxeq.1.220.pi. is the smallest positive root of the Bessel function J.sub.1 (x). This corresponds to an angular resolution equal to (j.sub.1 /.pi.)L/D.
The presence of atmospheric turbulence distorts the Airy pattern and increases the numerical value for the angular resolution to approximately (j.sub.1 /.pi.)L/s where s is the extent of the smallest optically significant atmospheric disturbance. At sea level typically s.apprxeq.0.1 meter. The extent s decreases with increased turbulence and increases with altitude. Since s&lt;&lt;D for typical large conventional telescopes, increasing the diameter of a telescope beyond s increases image brightness in proportion to D.sup.2 but the resolving power is not increased. The resolution of a single mirror telescope can only be increased by increasing its altitude by locating it on a mountain peak or in orbit about the Earth.
An alternate approach to achieving improved resolution of telescopes employs active optical imaging to compensate for atmospheric turbulence. Active optical imaging employs (1) an interferometric mechanism to measure the effective path-length error W(X,Y) that quantifies the atmospheric distortion as a function of objective plane X,Y coordinates, and (2) an activator mechanism to deform the objective surface of the telescope in the direction of the optical axis by W(X,Y)/2, thereby offsetting the atmospheric effects.
Multiple mirror telescopes are active optical imaging devices that eliminate the practical problems intrinsic to the construction and operation of a single large deformable mirror. FIG. 2 illustrates in plan view a conventional multiple mirror telescope 3 employing hexagonal shaped mirrors 4. Alternate designs may employ disks centered on points in a hexagonal lattice or squares centered on points in a square lattice. Practical telescopes require many times the number of mirrors illustrated in FIG. 2. Since D&lt;&lt;r, it is convenient to assume throughout the remainder of this disclosure that the surface of each mirror element of a multiple mirror telescope is planar.
The advantage of using hexagonal, rectangular, or triangular shaped mirror elements rather than disk-shaped mirror elements is that the objective surface of the telescope scope can be tiled using regular hexagons, rectangles or triangles, but the objective surface cannot be tiled using disks. An increase of 11.027% more light gathering power is attained by using mirror element shapes to tile the objective surface of the telescope compared with using circular discs.
The disadvantage of using hexagonal, rectangular, or triangular shaped mirror elements is that optical aberrations are introduced into the image by the linear edges of each element.